Effciency Measure Under Inter-Temporal Dependence

In this paper, a linear programming (LP) model is proposed to estimate the effciency of a decision-making unit (DMU) in the framework of dynamic Data Envelopment Analysis (DEA). Necessary and suffcient conditions required for characterizing dynamically effcient paths are established. An LP model is proposed to estimate the dynamic cost effciency (DCE) measure. It is proved that the aggregate CE in an assessment window is a convex combination of CEs of available periods in the assessment window. In addition, it is shown that a DMU in an assessment window is dynamically effcient when the DMU is dynamically cost/revenue effcient. Mathematical relationships between relative, cost, revenue, and profit effciencies are studied in the framework of dynamic DEA.